Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential
Asymptotics for Optimal Design Problems for the Schrödinger Equation with a Potential
We study the problem of optimal observability and prove time asymptotic observability estimates for the Schrödinger equation with a potential in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msup><mml:mfenced separators="|"><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow></mml:mfenced></mml:math>, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>⊂</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:math>, using spectral theory. An elegant way to model the problem using a time asymptotic observability constant is …